Exam 1. Econ520. Spring 2017

Transcription

1 Exam 1. Econ520. Spring 2017 Professor Luz Hendricks UNC Insrucions: Answer all quesions. Clearly number your answers. Wrie legibly. Do no wrie your answers on he quesion shees. Explain your answers do no jus sae hem. Show your derivaions do no jus sae he final resul. Do no refer o any noes or books. You may use a calculaor. The oal ime is 75 minues. The oal number of poins is

2 1 Shor Quesions (35 poins) 1. [9 poins] Explain why long-run growh is no susainable wih capial accumulaion only. Explain why i is susainable hrough knowledge accumulaion? Wha is he fundamenal difference? 2. [11 poins] Describe he reversal of forunes evidence. How does his evidence suppor he case ha insiuions are imporan sources of cross-counry income variaion? 3. [15 poins] In cross-counry daa, we see ha counries wih higher op marginal ax raes experience less income inequaliy. (a) Panel (a) of Figure 1 shows cross-counry evidence a one poin in ime. I would be emping o conclude ha axes cause inequaliy. Wha could go wrong wih ha argumen? Be specific. (b) Panel (b) shows changes over ime. How does his help address some of he issues ha Germany affec he Swizerland inerpreaion of panel (a)? Wha issues remain? Top 1 percen income share (percen) US UK Spain Norway Figure 1: Ireland Top marginal Porugal ax raes and income inequaliy (a) Cross-counry evidence Canada 12 Ireland Norway Germany 10 PorugalIaly Spain Ausralia NZ France Japan 8 Swizerland Finland Neherlands Sweden 6 4 Finland Ausralia NZ Sweden Denmark Denmark ( ) Neherlands France Canada Elasiciy = 1.90 (0.43) Top marginal ax rae (percen) Ialy Panel B. Top 1 percen share and op marginal ax rae in Japan UK US Figure 2. Top Income Shares and Top Marginal Tax Raes: Inernaional Evidence 254 AMERICAN (b) ECONOMIC Changes JOURNAL: over ECONOMIC imepolicy FEBRUARY 2014 Change in op 1 percen income share (poins) UK US Porugal Ireland Norway Canada Ialy Japan Elasiciy = 0.47 (0.11) NZ Ausralia Spain Sweden Denmark France Germany Finland Swizerland Neherlands Change in op marginal ax rae (poins) Noes: The figure depics he op 1 percen income shares and op income ax raes (including boh cenral and local governmen individual income axes) across 18 OECD counries in (panel A) and (panel B). Source for op income shares is he World Top Incomes Daabase. Source for op income ax raes is OECD and counry specific sources. If he counry does no have op income share daa for hose years, we selec he firs five years afer 1960 available and he mos recen five years (full deails in online Appendix A.2). For he following five counries, he daa sar afer 1960: Denmark (1980); Ireland (1975); Ialy (1974); Porugal (1976); Spain (1981). For Swizerland, he daa end in 1995 (hey end in 2005 or afer for all he oher counries). The figures repor he elasiciy esimae of he OLS regression of log(op 1 percen share) on log(1-mtr) based on he depiced dos. The correlaion beween op ax raes and op income shares is much sronger in han in Figure 3. Changes in Top Income Shares and Top Marginal Tax Raes Noes: The figure depics he change in op 1 percen income shares agains he change in op income ax rae from o based on Figure 2 daa for 18 OECD counries. The correlaion beween hose changes is very srong. The figure repors he elasiciy esimae of he OLS regression of log(op 1 percen share) on log(1 MTR) based on he depiced dos. op income shares. Among he counries which experienced significan op rae cus, some experience a large increase in op income shares (all five English-speaking counries bu also Norway and Porugal) while ohers experience only modes increases in op income shares (Japan). Ineresingly, no counry experiences a significan increase in op income shares wihou large op rae ax cus. The implied elasiciy from he OLS regression of he change in he log of he op reenion rae on he change of he log of he op 1 percen share is 0.47 and highly significan. Panel A in Table 2 repors esimaes from regressions of he form log(top 1 percen Income Shar e i ) = α + e log(1 Top MTR i ) + ε i on he complee ime series. Column 1 considers he full period , column 2 he early period and column 3 he mos recen period. Three lessons emerge. Firs, full period regressions generae esimaes around , highly significan, and robus o he inroducion of an overall ime rend or counry fixed 2 effecs. 37 Second, he implied elasiciy varies significanly across counries wih srong effecs in English-speaking counries, and paricularly he Unied Saes and he Unied Kingdom where he elasiciy is around 0.5, and much more modes effecs in oher counries such as Japan, Sweden, or Ialy, where he elasiciy is

3 2 Solow Model wih Land (28 poins) Consider a Solow model wih a fixed facor (land) denoed M. The producion funcion is and he law of moion for k = K/L is herefore Y = K α (A L ) β M 1 α β (1) k = sa β k α m 1 α β c (n + δ) k (2) where m = M/L and n is populaion growh. Assume ha A grows a a consan rae. Quesions: 1. [7 poins] Show ha he erm A β k α 1 Hin: How can g (k) be consan over ime? m 1 α β mus be consan on he balanced growh pah. 2. [7 poins] Show ha he balanced growh rae of capial is given by g (k) = βg(a) (1 α β)n. 1 α In he special case where α + β = 1, we are back in he sandard Solow model where g (k) = g (A). Hin: Wha is he growh rae of A β k α 1 m 1 α β? 3. [7 poins] The balanced growh rae of k may be negaive. How is his possible, given ha produciviy grows a a posiive rae? 4. [7 poins] Holding β/1 α fixed a 1, how does faser populaion growh affec he balanced growh rae of capial? Wha is he economic inuiion for his resul? 3

4 3 Romer Model wih Obsolescence (37 poins) Consider a Romer model where ideas become obsolee over ime. The rae a which his happens depends on he rae of innovaion. Specifically: A = B (s A L ) λ A φ δ (g (A )) A (3) where λ > 0, φ < 1, B > 0, and 0 < s A < 1 are parameers. The new par is he rae of obsolescence δ (g (A)), which is an increasing funcion of he growh rae of ideas. Quesions: 1. [8 poins] Derive he balanced growh rae of ideas. If you ge suck here, assume for he remainder of he quesion ha g ss (A) = λn 1 φ. 2. [7 poins] From here on assume ha λ = 1 and φ = 0. Derive he balanced growh level of A/L. Hin: You know g (A) from he previous answer. 3. [13 poins] For simpliciy assume ha δ (g (A)) = δ g (A) for some consan δ > 0. Graph how g (A) depends on A/L. Explain your graph. Wha does i say abou he sabiliy of he balanced growh pah? 4. [9 poins] Based on his graph, can you explain he odd resul ha δ affecs he balanced growh level of A/L, bu no he balanced growh rae? End of exam. 4

5 4 Answers 4.1 Answer: Shor quesions 1. The difference is rivalry. Boh ypes of capial are accumulaed subjec o diminishing reurns. Wihou some oher force o counerac diminishing reurns, he marginal produc of capial goes o zero as capial is accumulaed. Evenually, he MPK is oo small o suppor growh. Nonrival knowledge capial inroduces increasing reurns. Recall he example of a drug manufacurer. The increasing reurns offse he diminishing reurns ha se in as knowledge is accumulaed. 2. Reversal of forunes: Among colonies, we see a negaive relaionship beween incomes in 1500 and incomes and insiuions oday. The argumen: In low income colonies, populaion densiy was low. The only profiable sraegy was o sele. Thus, insiuions were pu in place ha proec he rule of law and individual righs. In high income colonies, slavery was he mos profiable sraegy. Hence, dicaorial insiuions were pu in place. 3. Income inequaliy and op ax raes: (a) The general poin: correlaion is no causaion. Wha could go wrong: Counries ha do no like high inequaliy could adop many policies aimed a reducing inequaliy (schooling, ransfers, ec). Think Sweden and Finland. (b) Using differences over ime addresses he poin made in (a). I is sill possible ha counries experience ime-varying shocks ha affec inequaliy. I is less clear why counries wih large shocks of his kind would choose large reducions in ax raes. A more plausible concern is: Perhaps counries ha reduced ax raes a lo also phased ou oher policies ha reduce inequaliy. 4.2 Answer: Solow Model wih Land All of his exacly follows he seps of he sandard Solow model. The inuiion is he same as for he model wih fixed resource inpus. In fac, his is a special case of he fixed resource model where he resource inpu is consan over ime. 1. g (k) = A β k α 1 m 1 α β only happen if he erm A β k α 1 c /k n δ. Balanced growh requires consan g (k). This can is consan over ime. m 1 α β 2. Take he growh rae of A β k α 1 m 1 α β and se i o zero. Solve for g (k). 3. The answer is he same as in he model wih non-renewable resources. Populaion growh implies ha m is falling over ime. This operaes like negaive produciviy growh. 4. If he share of land increases, g (k) falls. This happens because he fixed inpu is now more imporan in producion. A given reducion in m reduces oupu by more. I requires a larger increase in A o offse i. 5

6 4.3 Answer: Romer model wih obsolescence 1. The argumen is he same as in he sandard Romer model. 2. Sar from g (A) = Bs A L/A δ (g (A)) (4) On he BGP, g (A) = g ss = λn/ (1 φ). Then we have (A/L) ss = Bs A g ss + δ (g ss ) (5) 3. Now we have or g (A) = Bs A L/A δg (A) (6) g (A) = Bs AL/A 1 + δ We ge he usual graph, excep ha a higher δ shifs he g (A) curve down. 4. Remember how he balanced growh rae comes abou in he model wihou obsolescence. Wihou populaion growh, diminishing reurns lead growh o peer ou (moving along he g (A) curve). Populaion growh shifs he curve up a a rae deermined by n. This offses he diminishing reurns (scale effecs) and growh is susained a a rae ha also depends on n. The same happens here. A higher δ simply slows growh by a fixed amoun for any given A/L. To offse his, he economy mus lower he level of A/L (less diminishing reurns o A). The growh rae is sill deermined by he rae a which he g (A) curve shifs ou. (7) End of answers. 6